arXiv subjects

Marcus Mueller

Publications and source records attributed to Marcus Mueller.

At least 19 recordsLinked to original sources

arXiv2014

Mechanism of the Cassie-Wenzel transition via the atomistic and continuum string methods

The string method is a general and flexible strategy to compute the most probable transition path for an activated process (rare event). We apply here the atomistic string method in the density field to the Cassie-Wenzel transition, a central problem in the field of superhydrophobicity. We discuss in detail the mechanism of wetting of a submerged hydrophobic cavity of nanometer size and its dependence on the geometry of the cavity. Furthermore, we discuss the algorithmic analogies between the string method and CREaM [Giacomello et al., Phys. Rev. Lett. 109, 226102 (2012)], a method inspired by the string that allows for a faster and simpler computation of the mechanism and of the free-energy profiles of the wetting process. This approach is general and can be employed in mesoscale and macroscopic calculations.

cond-mat.stat-mech↗

arXiv2008

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter $q=Q^{*4} /T^*$, $Q^*$ is the reduced quadrupole moment of the molecule and $T^*$ the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of Perturbation Theory (PT) in the Mean Spherical Approximation (MSA). As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.

cond-mat.stat-mech↗

arXiv2006

Biological and synthetic membranes: What can be learned from a coarse-grained description?

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ simple and soft effective potentials, coarse-grained models can provide rather direct insight into collective phenomena in membranes on large time and length scales. We present a summary of recent progress in this rapidly evolving field, and pay special attention to model development and computational techniques. Applications of coarse-grained models to changes of the membrane topology are illustrated with studies of membrane fusion utilizing simulations and self-consistent field theory.

cond-mat.soft↗

arXiv2006

Accurate simulation estimates of cloud points of polydisperse fluids

We describe two distinct approaches to obtaining cloud point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand canonical ensemble. The first method determines the chemical potential distribution $μ(σ)$ (with $σ$ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution $ρ(σ)$ matches a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p(n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns $μ(σ)$ such that an equal peak weight criterion is satisfied for p(n)$ for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining $μ(σ)$. We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are {\em exponentially small} in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a novel polydisperse lattice gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.

cond-mat.stat-mech↗

arXiv2005

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model with Lennard-Jones interactions between the beads and a FENE potential between nearest neighbors along the backbone of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and non-equilibrium Molecular Dynamics simulations at constant temperature and volume using the Dissipative Particle Dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The viscosity and slippage at the interface are calculated as functions of grafting density and shear velocity.

cond-mat.soft↗

arXiv2005

Field Theoretic Study of Bilayer Membrane Fusion: II. Mechanism of a Stalk-Hole Complex

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first paper of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with system architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few $k_BT$ over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway.

cond-mat.soft↗

arXiv2005

Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends

We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the partition function of the interacting multi-chain systems in terms of integrals over auxiliary, often complex, fields, which are introduced by means of appropriate Hubbard-Stratonovich transformations. Thermodynamic averages like the average composition and the structure factor can be expressed exactly as averages of these fields. We discuss different analytical and numerical approaches to studying such a theory: The self-consistent field approach solves the integrals over the fluctuating fields in saddle-point approximation. Generalized random phase approximations allow to incorporate Gaussian fluctuations around the saddle point. Field theoretical polymer simulations are used to study the statistical mechanics of the full system with Complex Langevin or Monte Carlo methods. Unfortunately, they are hampered by the presence of a sign problem. In dense system, the latter can be avoided without losing essential physics by invoking a saddle point approximation for the complex field that couples to the total density. This leads to the external potential theory. We investigate the conditions under which this approximation is accurate. Finally, we discuss recent approaches to formulate realistic dynamical time evolution equations for such models. The methods are illustrated by two examples: A study of the fluctuation-induced formation of a polymeric microemulsion in a polymer-copolymer mixture, and a study of early-stage spinodal decomposition in a binary blend.

cond-mat.soft↗

arXiv2003

Field theoretic study of bilayer membrane fusion: I. Hemifusion mechanism

Self-consistent field theory is used to determine structural and energetic properties of metastable intermediates and unstable transition states involved in the standard stalk mechanism of bilayer membrane fusion. A microscopic model of flexible amphiphilic chains dissolved in hydrophilic solvent is employed to describe these self-assembled structures. We find that the barrier to formation of the initial stalk is much smaller than previously estimated by phenomenological theories. Therefore its creation it is not the rate limiting process. The barrier which is relevant is associated with the rather limited radial expansion of the stalk into a hemifusion diaphragm. It is strongly affected by the architecture of the amphiphile, decreasing as the effective spontaneous curvature of the amphiphile is made more negative. It is also reduced when the tension is increased. At high tension the fusion pore, created when a hole forms in the hemifusion diaphragm, expands without bound. At very low membrane tension, small fusion pores can be trapped in a flickering metastable state. Successful fusion is severely limited by the architecture of the lipids. If the effective spontaneous curvature is not sufficiently negative, fusion does not occur because metastable stalks, whose existence is a seemingly necessary prerequisite, do not form at all. However if the spontaneous curvature is too negative, stalks are so stable that fusion does not occur because the system is unstable either to a phase of stable radial stalks, or to an inverted-hexagonal phase induced by stable linear stalks. Our results on the architecture and tension needed for successful fusion are summarized in a phase diagram.

cond-mat.soft↗

arXiv2003

Interplay between wetting and phase behavior in binary polymer films and wedges: Monte Carlo simulations and mean field calculations

We study the interplay between wetting and miscibility of a symmetric polymer mixture via MC simulations and SCF calculations. The film surfaces interact with the monomers via short ranged potentials and the wetting transition is of first order. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. We investigate the dependence of the phase diagram on the film thickness D for antisymmetric surface fields. Upon decreasing the film thickness the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness D_tri there remains only a single critical point at symmetric composition. This corresponds to a second order interface localisation transition even though the wetting transition is of first order. At a specific film thickness, D_tri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analogon of the wetting transition of a planar surface, the latter is the analogon of the filling behavior of a single wedge. We present evidence for a second order interface localization transition in an antisymmetric double wedge and relate its unconventional critical behavior to the predictions of Parry et al. PRL 83 5535 (1999) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.

cond-mat.soft↗

arXiv2001

A Monte Carlo Test of the Fisher-Nakanishi-Scaling Theory for the Capillary Condensation Critical Point

Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H_1) in L x L x D Ising films of thickness D and two free L x L surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature T_c(D) and the associated critical field H_c(D) are estimated for 4 <= D <= 32 lattice spacings, for a choice of the surface field H_1 small enough that the dependence of H_c(D) on H_1 is still linear. It is shown that the results are consistent with the power laws predicted by Fisher and Nakanishi [M.E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely T_c(\infty)-T_c(D) \propto D^{-1/ν}, H_c(D) \propto D^{-(Δ-Δ_1)/ν}, where νis the bulk correlation length exponent of the three-dimensional Ising model, and Δ, Δ_1 are the corresponding ``gap exponents'' associated with bulk and surface fields, respectively. As expected, the order parameter of the thin film near its critical point exhibits critical behavior compatible with the universality class of the two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv1999

Symmetric Diblock Copolymers in Thin Films (I): Phase stability in Self-Consistent Field Calculations and Monte Carlo Simulations

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M.W. Matsen, J.Chem.Phys. {\bf 106}, 7781 (1997)], we study the ordered phases as a function of incompatibility $χ$ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from $χN=0$ to $χN=30$ and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.

cond-mat.stat-mech↗

arXiv1999

Symmetric Diblock Copolymers in Thin Films (II): Comparison of Profiles between Self-Consistent Field Calculations and Monte Carlo Simulations

The structure of lamellar phases of symmetric $AB$ diblock copolymers in a thin film is investigated. We quantitatively compare the composition profiles and profiles of individual segments in self-consistent field calculations with Monte Carlo simulations in the bond fluctuation model for chain length N=32 and $χN=30$. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Taking account of capillary waves, we find good quantitative agreement between the Monte Carlo simulations and the self-consistent field calculations. However, the fluctuations of the local interfacial position are strongly suppressed by confinement and mutual interactions between lamellae.

cond-mat.stat-mech↗

arXiv1999

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular paircorrelation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. We investiagte the temperature and composition dependence of the single chain conformations in symmetric and asymmetric blends and compare our findings to scaling arguments and detailed SCF calculations. Two aspects of the single chain dynamics in blends are discussed: the dynamics of short non--entangled chains in a binary blend and irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface. Pertinent off-lattice simulations and analytical theories are briefly discussed.

cond-mat.stat-mech↗

arXiv1998

Effect of long range forces on the interfacial profiles in thin binary polymer films

We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the apparent interfacial profiles. However, the apparent interfacial width cannot be described quantitatively by a simple logarithmic dependence on the film thickness. The Monte Carlo simulations reveal that the surface fields give rise to an additional reduction of the intrinsic interfacial width and an increase of the effective interfacial tension upon decreasing the film thickness. These modifications of the intrinsic interfacial properties are confirmed by self-consistent field calculations. Taking account of the thickness dependence of the intrinsic interfacial properties and the capillary wave broadening, we can describe our simulation results quantitatively.

cond-mat.stat-mech↗

arXiv1997

Interfaces between highly incompatible polymers of different stiffness: Monte Carlo simulations and self-consistent field calculations

We investigate interfacial properties between two highly incompatible polymers of different stiffness. The extensive Monte Carlo simulations of the binary polymer melt yield detailed interfacial profiles and the interfacial tension via an analysis of capillary fluctuations. We extract an effective Flory-Huggins parameter from the simulations, which is used in self-consistent field calculations. These take due account of the chain architecture via a partial enumeration of the single chain partition function, using chain conformations obtained by Monte Carlo simulations of the pure phases. The agreement between the simulations and self-consistent field calculations is almost quantitative, however we find deviations from the predictions of the Gaussian chain model for high incompatibilities or large stiffness. The interfacial width at very high incompatibilities is smaller than the prediction of the Gaussian chain model, and decreases upon increasing the statistical segment length of the semi-flexible component.

cond-mat.stat-mech↗

arXiv1997

Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin film geometry: A Monte-Carlo simulation

The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte-Carlo simulations of the bond fluctuation model of symmetric polymer mixtures. Both the canonical and semi-grand-canonical ensemble are studied. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the intrinsic profile) like sqrt{D}, before a crossover to a saturation value w_max (w_max^2 proportional to ln L) sets in. In the semi-grand-canonical ensemble, however, one finds the same widths (w proportional to sqrt{D}) as in the canonical ensemble for not too large L, while for large L the interfacial profile is smeared out over a finite fraction of the film thickness (w proportional to D for D -> infinity). We discuss the implications of these findings for the interpretation of both simulations and experiments.

cond-mat.stat-mech↗

arXiv1997

Reactions at polymer interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $ρ_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.

cond-mat.stat-mech↗

arXiv1994

Liquid-vapour asymmetry in pure fluids: A Monte Carlo simulation study

Monte Carlo simulations within the grand canonical ensemble are used to obtain the joint distribution of density and energy fluctuations $p_L(ρ,u)$ for two model fluids: a decorated lattice gas and a polymer system. In the near critical region the form of $p_L(ρ,u)$ is analysed using a mixed field finite-size-scaling theory that takes account of liquid-vapour asymmetry. Field mixing transformations are performed that map $p_L(ρ,u)$ onto the joint distribution of critical scaling operators \ptMEstar\ appropriate to the Ising fixed point. Carrying out this procedure permits a very accurate determination of the critical point parameters. By forming various projections of \ptMEstar , the full universal finite-size spectrum of the critical density and energy distributions of fluids is also obtained. In the sub-critical coexistence region, an examination is made of the influence of field mixing on the asymmetry of the density distribution.

cond-mat↗